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Relativistic Propulsion Using Directed Energy Johanna Biblea, Isabella Johanssona, Gary B

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Relativistic Propulsion Using Directed Energy Johanna Biblea, Isabella Johanssona, Gary B Relativistic Propulsion Using Directed Energy Johanna Biblea, Isabella Johanssona, Gary B. Hughesb, Philip M. Lubina aPhysics Department, University of California, Santa Barbara, CA 93106-9530; bStatistics Department, California Polytechnic State University, San Luis Obispo, CA 93407-0405 ABSTRACT We propose a directed energy orbital planetary defense system capable of heating the surface of potentially hazardous objects to the evaporation point as a futuristic but feasible approach to impact risk mitigation. The system is based on recent advances in high efficiency photonic systems. The system could also be used for propulsion of kinetic or nuclear tipped asteroid interceptors or other interplanetary spacecraft. A photon drive is possible using direct photon pressure on a spacecraft similar to a solar sail. Given a laser power of 70GW, a 100 kg craft can be propelled to 1AU in approximately 3 days achieving a speed of 0.4% the speed of light, and a 10,000 kg craft in approximately 30 days. We call the system DE-STAR for Directed Energy System for Targeting of Asteroids and exploRation. DE-STAR is a modular phased array of solid-state lasers, powered by photovoltaic conversion of sunlight. The system is scalable and completely modular so that sub elements can be built and tested as the technology matures. The sub elements can be immediately utilized for testing as well as other applications including space debris mitigation. The ultimate objective of DE-STAR would be to begin direct asteroid vaporization and orbital modification starting at distances beyond 1 AU. Using phased array technology to focus the beam, the surface spot temperature on the asteroid can be raised to more than 3000K, allowing evaporation of all known substances. Additional scientific uses of DE-STAR are also possible. Keywords: DE-STAR, Photon Drive, Directed Energy, Relativistic Travel, Interstellar Travel 1. INTRODUCTION Throughout history, scientists have expended significant effort researching possible methods for relativistic travel. Though numerous concepts have been proposed, we have yet to attain macroscopic relativistic travel. To date, the maximum spacecraft speed obtained is by the Voyager 1 spacecraft, at 17km/s (relative to the sun), as of the 2013-07-05 weekly mission report by JPL. This is only 5.7x10-5c. Figure 1. Artist conception of DE-STAR 4 propelling a spacecraft past Earth. DE-STAR is an orbiting platform consisting of a solar PV array, and a phased array of fiber laser amplifiers used primarily for asteroid orbit deflection. Reaction to ejected material provides a thrust that deflects the asteroid’s orbit. It could also be used for other scientific purposes, such as spacecraft propulsion, powering interplanetary spacecraft, asteroid composition interrogation, and space debris de-orbiting. 1.1 History of Relativistic Propulsion Research One of the earliest projects focused on relativistic travel was Project Orion1, studied in the early 1950s at Los Alamos National Laboratory. This proposed spacecraft used nuclear pulse propulsion, that is atomic bombs exploding behind the spacecraft, as their propulsion source. The resultant vehicle velocity expectation was between 0.08c and 0.1c. Concern regarding potential radioactive contamination resulted in the cancellation of the project. In 1973, the British Interplanetary Society initiated design of an unmanned interstellar spacecraft known as Project Daedalus2. The project, utilizing then current technology, proposed traveling 6 light years in approximately 50 years. Daedalus was a two-stage spacecraft design that employed fusion rockets. The first rocket stage obtained a projected speed of 0.071c over two years, and the second stage, spanning 1.8 years, achieved a cruising speed of 0.12c. The proposed Daedalus payload of 450 tons made it ideal for scientific research. The Daedalus project concluded that Interstellar flight is achievable. Between 1987 and 1988, the US Naval Academy and NASA developed Project Longshot3, a spacecraft utilizing nuclear pulse propulsion powered by nuclear fission. Project Longshot proposed a prospective trip to Alpha Centauri B at 0.045c, spanning 100 years. Other more exotic propulsion systems include antimatter propulsion such as the system proposed by Robert Forward of Hughes Research Laboratories4. Antimatter annihilation emits pions whose kinetic energy is then converted into thrust. The Marshall Space Flight Center has built antimatter traps5 (HiPAT), necessary for this engine, which store antiprotons for later use. Other areas of current thought that hold academic interest include gravity manipulation and warping of space-time. 1.2 History of Photon Propulsion The method of using a laser to propel spacecraft is not new, one proposed method would be to use a terrestrial laser6, while another method proposed by Robert L. Forward7 in 1984 suggests using a solar pumped laser. Forward proposes using a 1000km diameter Fresnel zone lens to focus the laser beam on the spacecraft composed of a mirror system weighing 1000kg. Further discussion by Young K. Bae8 describes the advantages of using a Photonic Laser Thruster (PLT) as opposed to more conventional engines to build an Interstellar Photonic Railway. This futuristic railway would compose of multiple manned space structures located along the "tracks" and used to propel spacecraft onward. 2. METHODOLOGY 2.1 DE-STAR While there have been many suggested methods of interstellar travel, the method we propose, in particular does not require on-board engines. Utilization of the DE-STAR 4, a conceptual space-based laser system9, as a photon drive, propels a 100kg spacecraft with a 30m diameter reflector to 0.6% the speed of light at the edge of the solar system. If we assume full reflector illumination at the edge of the solar system (roughly 900m diameter reflector) then we obtain 2% c, which is increased to 3% (21/2 times 2% c, see Section 2.3) with continued partial illumination for large distances. DE- STAR is a proposed modular system composed of an array of phase-locked lasers and powered by solar panels. With current technology, a DE-STAR 4 (104m per side) outputs an average of 70GW laser power. A reflector mounted at the rear of the spacecraft reflects incoming photons generating 470N thrust. In this paper, we demonstrate how directed energy from a DE-STAR could be used as a mechanism for relativistic propulsion, as depicted in Fig. 1. 2.2 Case I: Spot Size Smaller Than Reflector (Ds < D) As the spacecraft travels away from DE-STAR the spot size of the lasers will grow and eventually be larger than the reflector on the spacecraft. While the spot size is smaller than the reflector, it is straightforward to solve for time as a function of velocity. We know that the force due to the radiation pressure of the reflected laser beam is Pε F = r (1) c where P is the power at the spacecraft, and ε r =1+ ε where ε is the reflection coefficient, ε = 0 for no reflection (absorption) and ε =1 for complete reflection. We note that given an initial power, P0, from DE-STAR, relativistic effects must be taken into account. That is: Pε F = 0 r (2) γ c Since it is known that force is the derivative of the momentum, ρ = mv0γ , where m0 is the resting mass. Pε dρ 0 r = (3) γ cdt P0ε r ⎛⎞ddvγ =+mv0 ⎜⎟γ (4) γ cdvdt⎝⎠ Further simplifying, we obtain t in terms of the relativistic speed β = vc/ mc2 dβ t = 0 (5) ∫ 22 P0εβr (1− ) Which then solves to the analytical form 2 mc0 ⎛⎞β 11+ β t =+⎜⎟2 ln (6) 21P0ε r ⎝⎠−−ββ 21 mc2 ⎛⎞β 0 −1 (7) t =+⎜⎟2 tanh (β ) 21P0εβr ⎝⎠− We now can now invert our equation and obtain plots of β versus time. We plot the speed achieved by a 100kg spacecraft during various time intervals after initial propulsion by DE-STAR 4 in Fig. 2. The velocity is non-relativistic at early times followed by the transition to relativistic travel and ultimately reaching the relativistic limit. Figure 2. The left plot shows velocity versus time up to 10% c using the inverted equation for time (7), setting m0 = 100kg, P0 = 50GW, and ε r = 2 , and depicts the spacecraft traveling at non-relativistic velocities for the first 46 days. As the velocity increases, the spacecraft begins to display relativistic effects. At approximately 4 years, the velocity approaches its relativistic limit, c, shown in the right plot. This figure assumes a reflector size of sufficient diameter such that the spot size is always smaller than the reflector. At sufficiently large time, this becomes unrealistic for all known materials. These figures confirm that our equations obey the relativistic limit. For example, a time of 4.5x106s corresponds to a spot size (diameter) of 7.2x103meters and a time of 108s corresponds to a spot diameter of 2.7x106m. As a reality check, let us calculate how thick a reflector with diameter of 106m and mass of 100kg (as assumed in Fig. 2) must be. Given a density of 1g/cm3 we have a thickness of 10-13m, or 10-4nm. While this is not possible with current technology (Section 2.4) it may one day be possible with nano-technology, we discuss this further in Section 2.4. We can confirm the non-relativistic limit for β <<1 12+ β ∞ ln=→<<∑ βββ21n− 2 , 1 (8) 121−−β 1 n mc2 mvc ρ t →+==00()ββ (9) 2PPF00εεrr 4 As expected, for heavy spacecraft (large m0) the time to relativistic speed is longer. In the instance of a 10 kg spacecraft the speed remains non-relativistic even after 190 months, as shown in Fig. 3. 2 4 Figure 3. Plot of velocity versus time for m0 = 10 kg (blue dashed line) and m0 = 10 kg (red solid line) with P0 = 50GW and 8 ε r = 2 .
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